The goal of this section is to explain two algorithms that, given \(\epsilon \)  and a point \(Z\in {\rm Sym}(n,\) , return a point \(Z_\epsilon ^\mathcal {S}\)  (resp. \(Z_\epsilon ^\mathcal {B}\) ), a point close to the original point lying in the \(\epsilon \) -interior of the model. This is the equivalent of the projection applied in [1]} to constrain the embeddings to remain within the Poincaré ball, but adapted to the structure of the model. Observe that the projections are not conjugated through the Cayley transform.
